Tiresome duty for a judge (6)
I believe the answer is:
trying
'tiresome' is the definition.
(trying can mean annoying or tiresome)
'duty for a judge' is the wordplay.
'duty' becomes 'ing' (I can't explain this - if you can you should give a lot more credence to this answer).
'for' is a charade indicator (letters next to each other) (I've seen this in other clues).
'a judge' becomes 'try' (as in trialling a defendant).
'ing' after 'try' is 'TRYING'.
Can you help me to learn more?
(Other definitions for trying that I've seen before include "Making an effort - but annoying" , "Putting into dock" , "Testing" , "job for a jury?" , "Causing strain, annoying" .)